Question

Draw the graph of `y= |x-1|+3|x-2|-5|x-4|` and find the values of `lamda` for which the equation `f(x) = lamda` has roots of opposite sign.

Answer 1

We have `y=f(x) = |x-1|+ 3|x-2|- 5|x-4|`
`" "={{:(1-x+6-3x-20+5x",",, xlt1), (x-1+6-3x-20+5x",",,1le x le 2), (x-1+3x-6-20+5x",",,2 lt x lt 4),(x-1+3x-6+20-5x",",,xge 4):}`
`" "={{:(-13+x",",, xlt1), (-15+3x",",,1le x le 2), (-27+9x",",,2 lt x lt 4),(13-x",",,xge 4):}`
Graph of the function is as shown in the following figure.